Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
using namespace std;
long double b[1000];
long double ma = 1;
int main(){
	int a;

	cin >> a;
	for(int i = 0;i < a;i++){
		cin >> b[i];
	}
	sort(&b[0],&b[a]);
	for(int c = 0;c < a;c++){
		for(int d = 0;d < a;d++){
			if(c != d && (b[c] - b[d]) > 0){
				int g = (a-1);
				int h = (a-2);
			
			if(c != d && (c - d) > 0){
				int g = (a-1);
				int h = (a-2);
		
			if(g == c||g == d){
					g--;
					h--;
				}
			if(g == c||g == d){
					g--;
					h--;
				}
				if(h == c||h ==d) h--;

				double j = ((b[g]+b[h])/(b[c]-b[d]));
				if(ma < j){
					ma = j;
				}
			}
			}
	}
	}
	cout << fixed<< setprecision(5)<< ma<<endl;
	fflush(stdin);
	getchar();

		return 0;

}